Fractional continua for linear elasticity

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Authors

  • W. Sumelka Institute of Structural Engineering, Poznań University of Technology, Poland
  • T. Blaszczyk Institute of Mathematics, Częstochowa University of Technology, Poland

Abstract

Fractional continua is a generalisation of the classical continuum body. This new concept shows the application of fractional calculus in continuum mechanics. The advantage is that the obtained description is non-local. This natural non-locality is inherently a consequence of fractional derivative definition which is based on the interval, thus variates from the classical approach where the definition is given in a point. In the paper, the application of fractional continua to one-dimensional problem of linear elasticity under small deformation assumption is presented.

Keywords:

non-local models, fractional calculus